Description: A class is not equal to any of its elements. (Contributed by AV, 14-Jun-2022)
Ref | Expression | ||
---|---|---|---|
Assertion | elneq | |- ( A e. B -> A =/= B ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elirr | |- -. B e. B |
|
2 | nelelne | |- ( -. B e. B -> ( A e. B -> A =/= B ) ) |
|
3 | 1 2 | ax-mp | |- ( A e. B -> A =/= B ) |